Why does 13 divided by 0 not equal infinity?

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O rly?

Try this: http://www.wolframalpha.com/input/?i=lim%28x-%3E0%29+13%2Fx

It tends to +inf if approached from x>0 and to -inf if approached from x<0.

Look at that page again, it says that the two sided limit does not exist. lim x->a means the 2 sided limit.

Reply 41

BlueSam3

Original post by Elcano

Perhaps you misunderstood him?

lim(x->0) of 13/x tends to infinity - that should be true.

No it doesn't.

Original post by james22

Neither does 1/x

That at least has one sided limits.

Reply 42

Swayum

Original post by scrotgrot

"It is undefined" is a convenient semi-fiction to cover up the fact that maths basically doesn't work. 13/0 "is" infinity in a very meaningful sense, but then if you take that at face value and use it to make other assumptions about infinity other things don't work and the system breaks down, the simplest example is that if 13/0 = infinity = 2/0 then 13 = 2, so that all finite numbers equal each other.

In relation to infinity, all finite numbers DO equal each other: they are all infinitesimal. But essentially what it means is that infinity, insofar as it can be said to exist, must work on a different logic from the finite numbers.

So you either say there are two systems, which is iffy because you just derived one from the other, or you say infinity doesn't exist, which is also iffy because maths is supposed to be an entirely theoretical system defined on its own terms only.

Personally I think it's because the universe is a (necessarily) simplified simulation of itself running within (maybe any number of times removed) some true reality.

It is also true that a system cannot fully define itself using its own axioms, since the axioms are part of the system too. This is the same reason why we can never fully observe the universe and I also consider quantum logic to be another instantiation of the simulation thing.

Sorry, but do you have any idea what you're talking about? It seems like you're just making up random things here.

What on Earth does "it's because the universe is a (necessarily) simplified simulation of itself running within (maybe any number of times removed) some true reality" mean or how does it relate to infinity in actual mathematics?

Reply 43

techno-thriller

0 can go into 13 an infinite amount of times, so the answer is undefined

Reply 44

Zakee

What set does undefined occupy?

dun dun duuuuuuuuuuun.

Reply 45

rmhumphries

Original post by Zakee

What set does undefined occupy?

dun dun duuuuuuuuuuun.

Set S = {undefined}

Now at least, undefined occupies the set 'S' :h:

Reply 46

miser

There are two contradicting possibilities for a definition of n/0. The first one is that n/0 = positive infinity, since n divided by positive numbers approaching 0 increases the result until dividing by 0 yields positive infinity as a theoretical maximum. However, when we look at it from the opposite perspective we are given a different result. n divided by negative numbers approaching 0 decreases the result tending towards negative infinity.

It can be illustrated as follows:

5 / 1 = 5
5 / 0.5 = 10
5 / 0.25 = 20
...
Implying that 5 / 0 = positive infinity.

Yet:
5 / -1 = -5
5 / -0.5 = -10
5 / -0.25 = -20
...
Implying that 5 / 0 = negative infinity.

As such, it cannot be defined in a method consistent with the concept of division as it applies to other numbers.

(edited 10 years ago)

Reply 47

DannyYYYY

(edited 10 years ago)

Reply 48

mitchellshazia

People say this all the time on the basis that there are infinity zeroes in thirteen, and therefore 13/0 is infinity.
And while it is true that there are infinity zeroes in thirteen, the important point is that infinity zeroes aren't enough - because infinity zeroes is zero. You still need the thirteen.

It's like saying that 6/2 is 2, because there are two twos in six. And, yes, there are, but there's another one. So 6/2 is not 2. There are infinity zeroes in thirteen, but also some other stuff! Not just infinity zeroes!

(edited 10 years ago)

Reply 49

Mad Vlad

This should explain it...

Reply 50

Elcano

Original post by james22

Look at that page again, it says that the two sided limit does not exist. lim x->a means the 2 sided limit.

Can you read?

"It tends to +inf if approached from x>0 and to -inf if approached from x<0."

Reply 51

Felix Felicis

Original post by Elcano

Can you read?

"It tends to +inf if approached from x>0 and to -inf if approached from x<0."

Can you read? "The two-sided limit does not exist".

The notation

\lim_{x\to a} f(x) = L

is used to refer to the two-sided limit. The limit does not exist if it is dependent on which side you come from.

Reply 52

james22

Original post by Elcano

Can you read?

"It tends to +inf if approached from x>0 and to -inf if approached from x<0."

I can read. I know that, when taken from one side, the limit approaches infinity or -infinity. However you originally said that the limit existed, this is not true. I am doing my second year in a mathematics degree, I spent much of the first year doing this sort of thing. I know what I am talking about and you clearly do not.

Reply 53

james22

Original post by Elcano

Perhaps you misunderstood him?

lim(x->0) of 13/x tends to infinity - that should be true.

13/0 certainly isn't equal to infinity.

This was your original post that I replied to. What you have said is completely wrong and any mathematician would agree with me. The limit does not exist because it changes depending on which side you approach from.

Reply 54

Elcano

Original post by james22

Yes, it wasn't completely correct, I was missing a small plus. So it's not 'completely wrong'. And yes, I do know what I'm talking about, you're not the only guy at university. Are you satisfied now, or will you keep harping on it?

(edited 10 years ago)

Reply 55

james22

Original post by Elcano

Yes, it wasn't completely correct, I was missing a small plus. And yes, I do know what I'm talking about, you're not the only guy at university. Are you satisfied now, or will you keep harping on it?

You are the one who keeps quoting me, trying to show that you are still correct. That little + sign is pretty dam important in this case.

Really, this is very basic limit stuff. As has happened with other people, I wold understand making the slip up of asusming the limit was infinity. But you have been trying to defend your position when called out on it which shows either a complete lack of understanding, or an unwillingness to admit you are wrong.